Once you've authenticated with the Slack pack, you can send messages directly from inside your doc.
To do so, insert a button in the canvas or within a column (column type 'button'), and select 'Slack' as the button type. Then fill out each field in the button configuration.
To 'point' the button to a slack channel. enter # and the channel name in the field.
To point to a specific person, you can use their email address directly in the field. If you have a people column in the same table, you can point the field to "[Person].[Email]" as in the example below.